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Stage 2 · Algebra Part 1

Evaluate Functions

In math, "evaluate" can mean a few different things — sometimes it means solve, and other times it means substitute a value in and simplify. With functions, evaluating means substituting a given input for the variable and working out the result.

f(x) is just a shorthand for "plug in x and calculate." Once you see that, functions aren't scary — they're just substitution.

How do you want to start?

📖 Learn the Skill Lesson + examples ✏️ Foundations Practice Practice questions 🎯 GED Level Practice GED level questions

📖 The Lesson

When you see f(x), it means "a function called f, using the variable x." The rule inside the parentheses tells you what to do with x. Your job is always the same: substitute the given value for x and calculate.

What f(x) means
f(x) = 3x + 7
"f of x equals 3 times x plus 7." The letter f is just the name of the function. x is the input. When you're given a value like f(4), replace every x with 4 and calculate.
Other common names
g(x), h(x), f(t)
Functions can use any letter name. g(x), h(x), and f(t) all work the same way — substitute the value shown in the parentheses for the variable and calculate. The letter name doesn't change the process.
Worked Example — Linear Function

Given f(x) = 3x + 7, find f(4).

f(x) = 3x + 7
f(4) = 3(4) + 7
f(4) = 12 + 7
f(4) = 19
Worked Example — Quadratic with Negative Input

Given f(x) = −x² + 4x + 13, find f(−2).

f(x) = −x² + 4x + 13
f(−2) = −(−2)² + 4(−2) + 13
f(−2) = −(4) + (−8) + 13
f(−2) = −4 − 8 + 13
f(−2) = 1

⚠️ Calculator Warnings

Two calculator mistakes cause most errors on function problems. Know these before you start practicing.

✗ Wrong — no parentheses
−2² = −4

The calculator squares 2 first (getting 4), then negates it. That gives −4, which is wrong when you meant (−2)².

✓ Right — use parentheses
(−2)² = 4

Parentheses tell the calculator to square the negative number. (−2)² = (−2) × (−2) = 4. Always wrap negative inputs in parentheses before squaring.

Negative button vs subtraction button: When entering a negative input like −2, use the (−) negative button near the bottom of the calculator — not the subtraction button on the right side. They look similar but do different things. Using the subtraction button will cause an error.

🔄 Working Backwards Strategy

When a problem asks "which value of x makes f(x) = 13?", you don't have to solve the algebra. Instead, substitute each answer choice into the function and check which one works. This is faster and safer on a timed test.

Worked Example — Working Backwards

Given f(x) = 2x + 5, which value of x makes f(x) = 13? Choices: A) 3   B) 4   C) 5   D) 6

Test A: f(3) = 2(3) + 5 = 11 ✗
Test B: f(4) = 2(4) + 5 = 13 ✓
Answer: x = 4
Strategy tip: Start testing from the middle answer choice (B or C). If it's too high, try A. If it's too low, try C or D. This cuts down the number of substitutions you need to make.

✏️ Practice Questions

Bank 1 — Direct Evaluation
Questions are random — answer as many as you like
You've answered 5 questions. Keep going or check your score.
Bank 2 — Working Backwards
Questions are random — answer as many as you like
You've answered 5 questions. Keep going or check your score.
Up Next in Algebra Part 1
Solving 1 and 2-Step Equations
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